Question

Pyrolusite is a mineral containing manganese ions and oxide ions. Its structure can best be described as a body centered cubic array of manganese ions with two oxide ions inside the unit cell and two oxide ions each on two faces of the cubic unit cell. What is the charge on the manganese ions in pyrolusite?

Short answer

The charge on the manganese ions in pyrolusite is +3.

Step-by-step solution

Analyzing the structure of manganese in pyrolusite

Manganese occupies a body-centered cubic structure. First, find the number of ions at a normal body-centered cubic structure. There are eight manganese ions on the edges and one in the center of the unit cell, which means there are two manganese ions per unit.

$\left(8\times 1/8\right)+1=2$

There are two oxygen ions inside the unit cells and two on the face of the unit cell, meaning there are three oxygen atom ions.

$2+2\times 1/2=3$

Calculating the charge on the manganese ion in pyrolusite

Now set up a very simple algebraic equation to find the oxidation state of manganese. From the periodic table, the oxidation state of oxygen is -2. If there are two manganese and three oxygen ions, the oxidation state of the molecule is zero, and the oxidation state of manganese is X . Then:

$$\begin{gathered} 2X+3(-2)=0 \\ 2x-6=0 \\ x=+3 \end{gathered}$$

Thus the oxidation state of manganese is +3.